440 BELL SYSTEM TECHNICAL JOURNAL 



corresponding formulae which will be found useful in further applica- 

 tions. 



Part 1. Ideal Circuit Characteristics 



There is no distortion in the transmission of an impressed signal over 

 an electrical circuit or network when the shape of the received signal, 

 considered as a time-function with usually a time-of-transmission, is 

 identical with that of the impressed signal. A uniform decrease in 

 magnitude only is not distortion, and it can be restored to its original 

 value by means of a distortionless amplifier. 



Let us assume in the general case that the e.m.f. impressed on the 

 circuit is E, and that the circuit is always terminated by a receiver of 

 resistance, R, across which is the received voltage, v, in which we are 

 interested. The received current is then directly proportional to the 

 received voltage. 



The necessary and sufficient conditions for distortionless transmis- 

 sion can be stated quite simply in terms of the steady-periodic transfer 

 voltage ratio of the circuit which will be written as 



viiui) .. /.s 



with the terminology a -\- ih = the transfer voltage exponent of the 

 circuit, or concisely, the transfer exponent. Here a represents attenua- 

 tion in napiers and h phase difference in radians, omitting in the latter 

 any constant integral multiple of 2ir, and assuming the two voltages 

 to have zero phase difference at zero frequency. That is, the origin 

 of phase difference is so chosen that the phase intercept at zero fre- 

 quency is zero. 



For ideal transmission characteristics the steady -periodic transfer expo- 

 nent of the circuit should have an attenuation independent of frequency 

 and a phase proportional to angular frequency, w, ivhose slope is the time- 

 of-transmission of the circuit. 



In mathematical terms these ideal characteristics, represented by 

 primes, are 



a' = constant (napiers), 

 and (2) 



b' = TO) (radians), 

 where 



T = time-of-transmission (seconds). 



To show this, consider first what the indicial voltage, g{t), would be 

 under these assumptions. By indicial voltage is meant the received 

 voltage as a time-function per unit constant e.m.f. impressed at the 



